The utility of DGSPT is demonstrated in the context of three different applications. The first of these is a 2-dimensional map-based model for neuronal bursting known as the Chialvo map, introduced in [1]} and considered further in e.g. [2]}, [3]}. This map takes the standard form (REF ) in a suitable parameter regime, with an S-shaped critical manifold having two regular fold points and a flip-type (period-doubling) bifurcation in the layer map appearing as non-normally hyperbolic singularities on \(S\) . We show how DGSPT can be used to identify four open parameter sets corresponding to excitable, relaxation-type, non-chaotic bursting and (potentially chaotic) bursting dynamics. This analysis extends (in some directions) the work in [1]}, [2]}, [3]}, though it remains only partial since the dynamics near the non-normally hyperbolic fold points is not yet understood in detail.
